Re: does a matrix equivalent of the Arg function exist?

*To*: mathgroup at smc.vnet.net*Subject*: [mg53601] Re: does a matrix equivalent of the Arg function exist?*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Thu, 20 Jan 2005 03:47:42 -0500 (EST)*Organization*: Uni Leipzig*References*: <csl1af$6su$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, at least quaternions have a representation with angle and a 3d vector, but you can always define more than a single angle and for quaternions you may describe the 3d vector by the absolute value and the two angles of spherical coordinates, i.e. q={r*Cos[psi],r*Sin[psi]*Cos[phi]*Sin[theta],r*Sin[psi]*Sin[phi]*Sin[theta],r*Sin[psi]*Cos[theta]} Regards Jens "Roger Bagula" <tftn at earthlink.net> schrieb im Newsbeitrag news:csl1af$6su$1 at smc.vnet.net... > Arg[x+I*y] exists for any complex number. > The 2by2 Matrix: > {{x,-y},{y,x}} > behaves very much like the complex number. > With Euler matrices being three rotations by angles such that a total > angle exists, > it seems that an angle equivalency function like Arg should exist > generally for nbyn matrices as a kind of measure like the determinant. > Has anyone heard of such a matrix measure? > Any ideas about how to form such a function? > It would be useful geometrically in things like space and point groups > used in > crystalography and spectra of molecules. > -- > Respectfully, Roger L. Bagula > tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: > 619-5610814 : > alternative email: rlbtftn at netscape.net > URL : http://home.earthlink.net/~tftn >